How did Death get his ring back for 6x11 after 5x22 Swan Song?

But Death was already in possession of his ring when he made Dean the offer to do his job for a day. My guess is that Death must have retrieved it at some point between the end of season 5 and Appointment in Samarra.

that's because death asked dean for his ring back dean gave it to him the made the deal yad yada yada in the end dean gives deathe back the ring and sam get back his soul. i hope that answers you question

IM COMMENTING TWICE, HERE SO YOU GUYS CAN READ!-"Ok...im going to clear this up...in swan song(5x22), Dean meets up with death in chicago,to try to kill him for the ring, but death stops him, and explains he wants dean to have the ring. so he gives it under conditions to let sam say yes and jump...so time passes, sams back, without a soul, and dean decides he will summon death since he has leverage(having his ring). Now being death i guess the normal rules don't apply, because he does have power, but my guess is he is now limited. so dean makes a bet with death, to be death for one day, if he keeps the ring on, sam gets his soul back. if he removes it before 24 hours are up, sam doesnt get his soul. so dean takes the bet, learning that death had a motive to teach him a lesson, about natural order. when dean loses the bet, death, realizing dean had learned his lesson(also telling him to keep diging into this issue with souls(cas's plan)), Death gives sams soul back in turn, meanwhile taking his ring back off the table they're sitting at. Hope this helped you."